Let $\hat{a}$ and $\hat{b}$ be two unit vectors. If the vectors $\overrightarrow{c} = \hat{a} + 2 \hat{b}$ and $\overrightarrow{d} = 5 \hat{a} - 4 \hat{b}$ are perpendicular to each other, then the angle between $\hat{a}$ and $\hat{b}$ is

Question

( A ) $\frac{\pi}{2}$
( B ) $\frac{\pi}{6}$
( C ) $\frac{\pi}{4}$
( D ) $\frac{\pi}{3}$